In this chapter we will learn to subtraction rational number with same denominators with solved examples.
We have already shown the method to add the rational number with same denominator. Click the red link to learn that concept.
Subtracting rational numbers with same denominator
When we have rational numbers with same denominator, you simply have to subtract the numerators by keeping the denominator same.
For example, let a/b & c/b be the rational number with same denominator.
The subtraction is given as;
\mathtt{\Longrightarrow \frac{a}{b} -\frac{c}{b}}\\\ \\ \mathtt{\Longrightarrow \ \frac{a-c}{b}
Note that we have simply subtracted the numerator in this case.
I hope you have understood the concept. Let us now solve some problems.
Example 01
Subtract the rational number \mathtt{\frac{5}{3} -\frac{4}{3}}
Solution
Note that both the rational numbers have same denominator. Hence, we will simply subtract the numerator to get the right solution.
\mathtt{\Longrightarrow \frac{5}{3} -\frac{4}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5-4}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{3}}
Hence, 1/3 is the solution.
Example 02
Subtract the numbers \mathtt{\frac{10}{7} -\frac{8}{7}}
Solution
\mathtt{\Longrightarrow \frac{10}{7} -\frac{8}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{10-8}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{7}}
Hence, 2/7 is the solution.
Example 03
Subtract the rational number \mathtt{\frac{4}{15} -\frac{7}{15}}
Solution
Note that we have rational numbers with same denominator. So we will simply subtract the numerator to get the solution.
\mathtt{\Longrightarrow \frac{4}{15} -\frac{7}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4-7}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3}{15}}
Hence, -3/15 is the right solution.
Example 04
Subtract \mathtt{\frac{-8}{20} -\frac{9}{20}}
Solution
Note that the rational numbers have same denominator. So we will simply subtract the numerator to get the solution.
\mathtt{\Longrightarrow \frac{-8}{20} -\frac{9}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-8-9}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-17}{20}}
Hence, -17/20 is the solution.
Example 05
Subtract \mathtt{\frac{-15}{13} -\frac{-19}{13}}
Solution
Note that the multiplication of two negative numbers becomes positive.
\mathtt{\Longrightarrow \frac{-15}{13} +\frac{19}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-15+19}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{13}}
Hence, 4/13 is the solution.
Example 06
Subtract \mathtt{\frac{-3}{10} -\frac{2}{10}}
Solution
\mathtt{\Longrightarrow \frac{-3}{10} -\frac{2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3-2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-5}{10}}
The rational number can be further simplified by dividing numerator & denominator by 5.
\mathtt{\Longrightarrow \ \frac{-5\div 5}{10\div 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-1}{2}}
Hence, -1/2 is the right answer.